Step 1: Go buy If Chins Could Kill: Confessions of a B-Movie actor by Bruce Campbell.
This book is indispensible for anyone looking to start in film. Plus....well....he's Ash, and you're making a zombie flick. There's also make-up tips and such in it.
As for the actual movie, make sure you've got a good base script. I know that in horror, writing is overlooked in favour of effects, but trust me, the plot does matter.
Be creative,be inventive, and have fun.